# Money weighted Vs Time Weighted Return

An investor started the year with a \$10,000 portfolio. He made a \$1,000 contribution at the end of the first quarter, a \$2,000 withdrawal at the end of the third quarter, and ended the year with a portfolio value of \$10,553. The quarterly holding period returns for the investor’s portfolio are as follows. Q1 Q2 Q3 Q4 3% -5% 8% 10% The money-weighted and time-weighted returns for the year are closest to: Money-Weighted Time-Weighted a. –4.66% 3.84% b. 3.59% 3.84% c. 14.34% 16.25% d. 16.00% 16.25%

I’ll go with C. Time weighted = (1.03*.95*1.08*1.1)-1= 16.25% Money weighted = CF0=-10000, CF1=-1000 CF2=0 CF3=2000 CF4=10533 CPT->IRR-> 3.58% 3.58%*4=14.34%

Will go with C as well

I think the answer is B as Time weighted is exactly same as Geometric mean and my answer is 3.84%. What is the answer?

the answer is C. Remember that the time series is per quarter. so you do not raise to the power 1/4 to get 3.84%. It has to be the full year’s which is 16.25% For the money weighted – you get a quarter’s worth which is 3.84 – so multiply by 4 to get 14.34%.

To double check your time-weighted return, assume no contributions or withdrawals were made. In that case, the portfolio starts with \$10,000 and ends with \$11,624, a return of 16.24%. The assets in the portfolio returned 16.24%, but the investor took out some money and lowred his/her return. For the money-weighted return, it is an IRR problem with cash flows timed quarterly.

Not sure what I am doing wrong but my BAII Plus professional calculator keeps giving me 3.54% and hence 14.167% as the IRR. Can someone point out what I might be doing wrong. I got the answer as C but slightly skewed results.

I got B as well… The money weighted return (MWR) is just the IRR in which you (Long onCFA) calculated. The time weighted return is the geometric mean in which I got the following: {(1.03)(.95)(1.08)(1.1) }^(1/4) -1 = 3.84. Hence the answer that I got is a B.

Guys…its asking for annual return…not quarterly.